Questions tagged [quantum-chemistry]
The quantum-chemistry tag has no usage guidance.
283
questions
3
votes
1
answer
66
views
Multi-electron Bloch bundles over powers of the Brillouin torus?
The quantum states of single electrons in a crystal famously form a (Hilbert) vector bundle over the Brillouin torus ${\mathbb{T}}^d$ -- the Bloch bundle.
Does this theory usefully generalize to ...
- 13k
1
vote
0
answers
21
views
Finding a bound on ground state energy derivatives of molecule
Part of a project I'm working on involves exploring the smoothness of the ground state energy $E(x)$ of a molecule where $E$ is parameterized by the geometry of the molecule. In particular, my goal ...
0
votes
0
answers
15
views
What is the single active electron approximation?
I keep stumbling upon this approximation while reading papers on atomic physics, but I couldn't find a proper description of what it is in any textbook or pedagogical paper. The closest I could find ...
- 3,731
0
votes
1
answer
39
views
QM: How do electrons affect each other's potential energy?
I'm trying to learn quantum mechanics. And I'm confused.
The question is, do electrons affect each other's wave functions, i.e. potential energies?
How do they affect each other orbital shapes, how do ...
- 3
0
votes
1
answer
46
views
The uncertainty principle and the quantization of electron momentum in orbitals - Why are larger energy gaps considered more uncertain?
I am a chemist trying to understand how the uncertainty principle can be applied to the mechanics of atomic and molecular orbitals in order to have better intuitions about stability and reactivity. ...
0
votes
0
answers
21
views
Are the concepts of activation energy and collision theory applicable for this reaction?
This is the reaction:
$$\text{2Na(s)}+\text{Cl}_2\text{(g)}\longrightarrow \text{2NaCl(s)}\tag{1}$$
This is a reaction between a solid (sodium metal) and a gas (chlorine gas). According to Britannica,
...
- 754
0
votes
0
answers
49
views
Is ionization energy non-negotiable?
$$\text{2Na(s)}+\text{Cl}_2\text{(g)}\longrightarrow \text{2NaCl(s)}\tag{1}$$
This is a spontaneous reaction ($\Delta G<0$). 2 Na atoms donate 2 electrons to 2 Cl atoms.
However, Na still has a ...
- 754
2
votes
0
answers
17
views
How does the concept of activation energy work for interatomic collisions?
Say we have a Lennard-Jones -esque potential for colliding atoms. Say this potential admits a bound state at a lower energy than the kinetic energy of the colliding atoms. So forming this molecule ...
- 21
0
votes
1
answer
30
views
Does the copper normalize?
I am reading Concepts of Elemental Particle Physics. In it, it describes what happens when a high energy muon is shot into a copper rod. An electron is is knocked out of its orbit and and photons ...
- 2,371
0
votes
1
answer
48
views
Excitation of electrons from $3p$ to $3d$ in sulphur
In my book it is shown that sulphur in its excited state forms 6 covalent bonds with Fluorine to form SF6 but after the electron is excited does it not dexcite from $3d$ back to $3p$ and $3s$ by ...
- 139
1
vote
1
answer
69
views
Why do some atoms like Mg have several ionization energy levels?
In Dopant Energy Levels in Crystalline Silicon (which asks for a password, but is partially readable if you click "cancel") appears the following image and caption:
Figure 2777b shows the ...
- 23
0
votes
0
answers
47
views
Schrodinger operator with matrix potential and Green's function
Clearly Schrodinger operators with matrix potentials appear very naturally in molecular dynamics/quantum chemistry, particularly when considering a crude adiabatic basis or diabatic basis for an ...
1
vote
0
answers
64
views
Why is octaoxygen diamagnetic?
I tried considering that according to LCAO-MO theory $O_2$ is paramagnetic, which is confirmed by experimental evidence. Since octaoxygen has the crystal structure in figure, I thought there is a kind ...
- 111
1
vote
2
answers
65
views
On non-existence of molecular helium (and or why that's equivalent to bond order zero)
Why does molecular orbital theory (MOT) imply that molecular helium does not exist? All answers I found in the web use following two standard arguments, but I not see why these are sufficient to ...
- 89
-4
votes
1
answer
143
views
Who first modelled water as a tetrahedron?
Who first modelled water as a tetrahedron? In this model the oxygen is at the center and the two hydrogens are at the vertices (I think, or maybe somewhere along the edges?).
Source
This gives the ...
- 1,359
0
votes
1
answer
40
views
What prevents us from designing material or catalysts to meet the custom requirements? [closed]
From the perspective of physics, everything is made of atoms, ions, electrons, etc. Since we know the basic interaction between elementary particles, it might be possible to design customized ...
- 575
2
votes
1
answer
183
views
Atom orbitals physics vs. chemistry
Why draw chemists always $|2p_x\rangle$, $|2p_y\rangle$ and $|2p_z\rangle$ orbitals instead of $|2,1,m\rangle$?
Since $|2p_x\rangle$ or $|2p_y\rangle$ are a superposition of energy eigenstates they ...
- 349
0
votes
0
answers
23
views
Ultra-Low Temperature semiconductors
What benefits does cooling semiconductors have for technology or any other innovations? I understand semiconductors can become good conductors at high temperatures which are ideal for everyday things ...
- 11
1
vote
0
answers
43
views
Why does inversion symmetry disallow valence band maximum (VBM) to conduction band minimum (CBM) electronic transitions?
I have somewhere read that due to inversion symmetry in the crystal structure the electronic transition occurs from some bands below VBM and therefore optical band gap comes into the picture with a ...
- 21
2
votes
1
answer
39
views
Cooperative orders
I am familiar with the more "traditional" types of order and their corresponding degrees of freedom one might find in a many-body system, such as crystalline (translational d.o.f.), ...
- 207
3
votes
1
answer
72
views
What steps are exact in Born-Oppenheimer and adiabatic approximation?
I am reading about adiabatic and Born-Oppenheimer approximation and I can't understand what steps are exact and what steps are approximations.
Both these approximations are based on the idea that as ...
- 1,312
0
votes
1
answer
131
views
Quantum mechanical model of benzene ring [closed]
The infinite square well scenario can be used to model the $\pi$-electrons of a benzene ring. It can be shown that the eigenfunctions of the ring can be written as
$\Psi_{n}(x) = \frac{1}{\sqrt{L}}e^{\...
- 7
0
votes
1
answer
38
views
Solving to get the kinetic energy integral for restricted closed shell hartree fock calculations
The Kinetic energy integral given in the book Modern Quantum Chemistry by Attila Szabo and Neil Ostlund is given by (Appendix A eqn A.10)
$$
\left(A\left|-\frac{1}{2} \nabla^{2}\right| B\right)=\int d ...
- 29
1
vote
1
answer
82
views
Why does a neutral atom have no external electric field?
I've been trying to find an answer to this for some time now. In advance, I imagine the orbital model, nevertheless I cannot imagine that if I am for example closer to a side of the atom, the dipole ...
- 165
1
vote
1
answer
45
views
Showing that the creation operator is a spin tensor operator
In the second quantization formalism of quantum chemistry, according to the book 1 on page 43, the creation operators $a_{p,\beta}^{\dagger},a_{p,\beta}^{\dagger}$ satisfy the relations
$[\hat S_\pm,...
- 234
0
votes
1
answer
45
views
How to express atomic states 1S, 1D, 3P in terms of spherical harmonics or cubic harmonics?
Textbook state that, because of Pauli principle and anti-symmetry of wave-function, only 1S, 3P, 1D with totally $C_6^2=15$ states are allowed for 2 electrons $np^2$ state. My question is how to ...
- 1
0
votes
1
answer
43
views
A poorly posed time dependent perturbation benzene type ring question
In my first year masters QM class my professor recently mentioned an example that he said he would either give on an assignment or possibly put on our exam. We have all our assignments now and it hasn'...
0
votes
0
answers
28
views
Probabilities fall outside the differential?
A few years ago I had a conversation with a physical chemist, and one of her comments still lingers in my memory. Our conversation was about Quantum Chemistry. In response to my commenting on the ...
- 158
0
votes
0
answers
51
views
What do chi ($χ$), psi ($ψ$), and capital gamma ($Γ$) stand for in these equations about molecular geometry (combination bands and overtones)?
Special case
If one of the symmetries is doubly degenerate in the excited state a recursion formula is required to determine the symmetry of the $v$th wave function, given by,
$$\chi _{v}(R) = \frac{1}...
- 3,443
0
votes
0
answers
20
views
Implementing symmetry in MRCI calculation
I am running Multi Reference Configuration Interaction calculations for Aluminium Flouride molecule in its A1Pi state interacting with Helium. For a complete Potential energy surface, i am doing the ...
0
votes
1
answer
61
views
Can different electron orbitals within the same atom be entangled?
Could the electron in the outer shell orbital be entangled with an electron within the inner S orbit of the atom? If so, how would this affect the properties of such an atom, such as emission and ...
- 409
2
votes
0
answers
39
views
In molecular orbital theory for $H_2^+$, why do we only add or subtract orbitals but never alter one of the phases of the orbitals?
EDIT and TLDR: Atkins' physical chemistry contains the quote "In general, from N atomic orbitals we can build N molecular orbitals". In the case of $H^+_2$, we use a combination of N=2 ...
- 1,175
0
votes
1
answer
54
views
Relation between Photochemical reactions and Photoelectric effect
I was writing my lab report of determining the value of Planck's Constant using photoelectric effect. Suddenly, a question stuck my mind that in photoelectric effect electrons are ejected from ...
- 3
1
vote
1
answer
99
views
Quantum mechanical description of how bonding works?
I am trying to conceptualize of chemical bonding, and really be able to explain to someone with lots of questions how exactly it works. I am having a hard time conceptualizing what the bonding is ...
- 1,978
1
vote
1
answer
65
views
Relationship between quantum chemistry and physics Hartree-fock approaches
In standard quantum chemistry books (e.g., Szabo Ostlund), Hartree-Fock is usually introduced from a first quantized picture. Given molecular orbitals $\psi_a(\mathbf{r})$ that are expanded in terms ...
- 111
0
votes
2
answers
75
views
Why energy expectation values (Energy) are functions of coefficients of corresponding trial wave functions in variational principle?
The method consists of choosing a "trial wavefunction" depending on one or more parameters and finding the values of these parameters for which the expectation value of the energy is the ...
0
votes
0
answers
29
views
Doing chemistry with atoms or "Renormalization group on chemistry"
When I studied molecular mechanics we saw all of this in terms of electrons with classical nucleus. Is there a formulation in term of atoms-as-particles (ignoring internal structure, but maybe taking ...
- 94
0
votes
0
answers
16
views
Ionization potential for surfaces
For an isolated structure, like a molecule, the ionization potential can be computed using total energies obtained from DFT:
$$IP = E(N) - E(N-1).$$
But what if I have a structure finite in one ...
- 1,496
3
votes
0
answers
62
views
Computing the 2-electron Reduced Density Matrix (2RDM) using QED
So in quantum chemistry there is this concept of the 2-electron Reduced Density Matrix (2RDM), denoted here as $\Gamma$. It is defined, more like a function than a matrix, as the ridiculous integral ...
- 272
1
vote
0
answers
37
views
Why does the energy of an atomic orbital depend on the proximity to charges?
I was recently reading about Crystal field theory and especially crystal field splitting in the context of transition metals in coordination complexes. Here is what I think I have understood – or what ...
- 3,568
1
vote
0
answers
27
views
Calculating the Franck-Condon Factors
I want to calculate the Frank-Condon Factors using the standard equation:
$$q_{v'v''}=\left[\int \psi_{v'}^* \psi_{v''} dr\right]^2$$
I have the vibrational wave functions of $v'$ and $v''$ in ...
- 11
0
votes
0
answers
19
views
Transition Dipole Moment Function
A simple question: I have came across the word "transition dipole moment function" many times. I have seen it in Einstein coefficient relation or also called transition rates. In this ...
- 197
7
votes
4
answers
1k
views
Are all waves periodic?
I'm studying waves, and I am confused about two different definitions of a wave. One place defines a wave as "a propagating dynamic disturbance of one or more quantities". Another says that &...
1
vote
0
answers
31
views
Linear combination of atomic orbitals
For example, I have linear combination of states $$|n,l,m\rangle:~| \psi \rangle = c_1 |2,1,0\rangle + c_2 |2,1,-1\rangle +c_3 |2,1,1\rangle $$. Here $n =2$, $l = 1$, so it's three p-orbitals with ...
- 11
0
votes
2
answers
32
views
Can ionic bonds only have discrete distances?
If 2 atoms have an ionic bond, can they only be certain distances apart just like an electron can only be in discrete shells around the nucleus?
In other words, are ionic bonds quantum?
- 335
4
votes
3
answers
297
views
Why do molecules behave classically at high temperatures?
In chapter 6 of "Charge and Energy Transfer Dynamics in Molecular Systems", the authors consider diatomic molecules in contact with a heat bath. We have established before that the nuclear ...
- 857
0
votes
1
answer
95
views
What is the IRREP of the $p_z$ orbital in a $C_s$ point group?
What is the representation on the $p_z$ orbital in a $C_s$ symmetry group?
The $C_s$ symmetric group has two irreducible no. of representations
$A^{'}$ ---> $s, x, y, xy$ and
$A^{''}$ ---> $...
1
vote
0
answers
53
views
Second quantization for atomic or molecular models
I'm trying to learn QED in the context of quantum chemistry (ie to model relativistic effects for heavy atoms) and I'm struggling conceptually with second quantization: specifically, what is the ...
- 81
0
votes
1
answer
22
views
Why does the transmission of a material depend on its wavelength?
my question is pretty much in the title 'Why does the transmission of a material depend on its wavelength?' I know it's to do with electrodynamics and solid-state physics. I was just hoping someone ...
- 15
1
vote
1
answer
205
views
Lagrangian of a Hydrogen Atom
So in classical mechanics, we can generally convert from the Hamiltonian to the Lagrangian and back using Legendre transformations. However, I have found this to be a bit troublesome in QM. ...
- 480